#Question About Independence In linear algebra

6 messages · Page 1 of 1 (latest)

icy stone
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So my question is
Lets say we are given 3 vectors and we are asked to check if they are independent.. those 3 vectors belong to R^4... Doesn't that mean that because we are given 3 vectors we are gonna get a 4x3 matrix.... But then by doing gauss elimination to check if there is a dependent column we are always going to find that the last row will be zero meaning that at least the last column is gonna be dependent? Because the last row will always be 000 since we dont have enough vectors to form a long enough matrix? Am i missing something?

last rivetBOT
icy stone
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Or is that not correct and i should always do gauss elimination to check?

sleek quartz
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It doesn't matter if you have a 4 x 4 or 4 × 3 matrix or whatever (except 4 × b, b > 4, the vectors will always be linearly dependent)

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It's enough to see if you find any zero-rows / colomns

exotic sleet
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.close